Nowadays tomographic reconstruction has become a widely used technique for structure determinations in medical and biological applications. Macromolecules such as proteins and nucleic acids are important biological macromolecules, which possess important functional information within their structure. In addition, most biological macromolecules including proteins are flexible, with enhanced ability to interact with other molecules. As such, structure determination has important applications especially for purposes of understanding interactions between molecules, and thus, is of vital importance in drug development.
Many standard 3D structure determination techniques, such as x-ray crystallography, nuclear magnetic resonance (NMR) or single particle cryo-electron microscopyare, are based on averaging, which may cause losses of most information about the conformation or flexibility of the macromolecular structure. To overcome this problem, cryo-electron tomography (Cryo-ET) is introduced, which involves taking transmission electron microscope (TEM) images of a cryo-specimen at different tilt angles and reconstructing a 3D tomogram through aligning and back projecting the different images. Cryo-ET preserves the native structure of molecules due to rapid freezing to liquid nitrogen temperature, and does not necessarily involve averaging. As a result, it enables a thorough study of flexible multi-domain proteins in the native state.
Cryo-ET 3D reconstructions of macromolecules encounter several types of noise. One type of noise is specimen noise, which is mainly due to rearrangement of the specimen during data recording or degradation due to electron beam damage. This type of noise is normally minimized using a sufficiently low dose. The low dose, however, increases the uncorrelated shot noise caused by low illumination. In addition, correlated noise can appear due to imperfections of the TEM detector. This is because, normally, a gain reference is created to equalize the responses from individual detector elements, but errors in the gain reference can give rise to noise that is correlated with a region of the detector rather than with the specimen.
Most uncorrelated shot noise in cryo-ET reconstructions can be significantly reduced using procedures for regularized refinement, such as constrained maximum entropy tomography (COMET). In medical applications the shot noise is generally avoided to a large extent since a high dose could be used. However, correlated noise emanating from the detector measurement is difficult to handle since this kind of noise is related to sensitivity variations across the detector surface. To ensure homogenous signal responses, flat-fielding is often used in practice, but given the variations in the quality of flat-fielding, the resulting base-line comes with variations. The variations around the base-line result in a position-correlated noise, which, in a 2D or 3D reconstruction, causes an increased background in a position dependent on the length of the direction orthogonal to the detector surface, or for many projections, in the untilted beam direction.
In light of the above, there is a need for improved techniques to remove correlated noise for enhanced three-dimensional (3D) reconstruction images.